that the lower rate of population growth of r} leads to a lower income per worker than the greater rate of population growth r2.
Expenditures on education in most cases will probably not increase in direct proportion to the number of young people in the population.* Taxing capacity will depend somewhat on real income per person. There are many alternative claims on public revenues. These conflicting claims will vary with the rate and pattern of population growth. In a largely agricultural population, the greater the rate of population growth, the less land per man; the greater the degree of fragmentation of holdings, and usually the smaller the output per man. Also, high growth rates will normally increase the burden of dependency (9, pp. 332-333) and decrease potential taxable revenues. Population growth may raise population replacements to a higher production capacity per person, other things equal, but it may simultaneously make it more difficult to provide a given amount of education for the same proportion of children entering the population (9, pp. 247-249).
Intuitively we should expect that as population grows, beyond some rate, that education per person declines. Under this assumption we have two opposing forces at work. On the one hand, a greater rate of population growth yields a greater replacement effect, but on the other hand, a greater rate of population growth reduces education per person. In principle, the balance of forces can still be in favor of the replacement effect. Thus in Figure 3 the intermediate rate of population growth r2 yields the highest income per worker, t
Educational inputs are unlike traditional inputs. Although we know in a general way that education pays off from a productivity viewpoint, we do not know much about the marginal productivity of education. Calculations of the returns to education have been of the average returns to marginal years of education. What we do not know very much about are the marginal returns to marginal years of education. The author's view is that it is not at all impossible that the marginal returns for some marginal years of education may be zero when a given type of education expands very rapidly.+ Education is also complicated by the fact that its inputs are diverse, its quality is rarely constant, and many of its influences on productivity are indirect. This may be one of the reasons why very general types of education, which frequently
*See (28) and Gavin Jones, "Effect of Population Change on the Attainment of Educational Goals in the Developing Countries," in this volume.
* TJ, r2, and r3 are rates of population growth associated with the alternate amounts of labor force increase L0Lt, or L0L2, or LQL3.
•!-An unpublished study by the author on returns to education in Greece leads him to believe that this may have occurred with respect to secondary education for the period